Question

A particle rotates in horizontal circle of radius 'R' in a conical funnel, with speed 'V'. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is ______.

(g = acceleration due to gravity)

Options

• `V^2/(2g)`

• `V/g`

• `V^2/g`

• `V/(2g)`

Answer 1

A particle rotates in horizontal circle of radius 'R' in a conical funnel, with speed 'V'. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is `underline(V^2/g)`.

Explanation:

N sin θ = mg

`"N" costheta="mV"^2/"R"`

`therefore costheta="V"^2/"Rg"`

`therefore"h"/g="V"^2/"Rg"`

`therefore"h"="V"^2/g`